Problem: If $\frac{1}{4}$ of $2^{30}$ is $4^x$, then what is the value of $x$ ?
Answer: We have $\frac{1}{4} \cdot 2^{30} = \frac{2^{30}}{2^2} = 2^{30-2} = 2^{28}$.  We also have $4^{x} = (2^2)^x = 2^{2x}$.  Setting these equal gives $2^{28} = 2^{2x}$, so $2x =28$, which means $x = \boxed{14}$.